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There’s time for one more debate here, about my Earth Day column, but first an announcement: After three years of experiments, TierneyLab is shutting down. I’ll still be testing ideas in my Findings columns and in other articles for The Times, and you can keep up with them by following me on Twitter. You can also keep trying the weekly math puzzle at its new home starting next Monday at The Times Wordplay blog.

I’ll miss our debates here — well, most of them, anyway — but I like to think we can have even better ones now that I’ll be concentrating on my columns and on longer articles (and there will be plenty of opportunity for you to dispute them). As much as I enjoyed doing the blog, I found myself wanting the opportunity to delve more deeply into subjects. Contrarianism tends to be time-consuming.

When I was working on a column last year about the science of concentration, I got some advice from Winifred Gallagher, the author of “Rapt”: At the start of your workday, ignore all short-term distractions (e-mail, blogs, etc) and devote 90 solid minutes to your most important project. It seemed like an excellent rule, but I kept violating it because my day always began with a blog in need of filling. I realized other writers managed to balance blogs with longer articles, but I finally decided that sort of multitasking was beyond me.

So this is the last post. I welcome any thoughts you have on my latest Findings column about lessons for Turqs, which is Stewart Brand’s term for scientifically inclined greens. Is Turq a good term, or do you have a better one in mind? Are there other lessons that environmentalists should have learned since the first Earth Day?

I also welcome any general thoughts you have on the Lab, and I want to thank you for all the wisdom and wit and passion you’ve shared over the past three years here. Special thanks go to the scientists who provided posts and quizzes for Lab readers, and to my Times colleagues who contributed posts and helped run the Lab, notably Jim Gorman, the blog’s editor, and Thomas Lin, Sarah Graham and Ken Chang.

One of the great joys of the Lab was watching readers solve the math puzzles by working together in a collaboratory, as it was described by one of the early solvers: the incomparable Pradeep Mutalik. Once it became clear how brilliant Pradeep was at both solving and creating puzzles, I was happy step aside and let the Quiz Wiz handle the Monday Puzzle. Thanks, Pradeep, for all the clever mathematical and linguistic pleasures pleasures you’ve provided (and thanks for your very kind farewell puzzle). Thanks also to Justin Thyme, for all the deft puzzle illustrations plus the wonderful TierneyBlab meta-blog. To repeat, you can enjoy their puzzles and illustrations every Monday at Wordplay , and you can follow me on Twitter.

Each of these puzzles is an arithmetic sum with letters standing in for digits, in one-to-one correspondence. An individual letter represents the same digit wherever it occurs in a given puzzle, but could represent a different digit in the other puzzles. Try not to use a computer program. Happy solving!

The Monday Puzzle is on the move. TierneyLab is about to shut down (John explains here why he’s closing the blog to concentrate on longer articles and his science column), but the math puzzles will continue at a new home, The Times’ WordPlay blog. The math puzzles by me with illustrations by Justin Thyme will appear there under the title “Numberplay” starting next Monday. This is the last puzzle here at the Lab, so it is time to take a stroll down memory lane . . .

My first association with John Tierney and the TierneyLab Monday Puzzle took place just over a year ago, when, as a general reader, I took part in the God-Einstein-Oppenheimer Dice puzzle of March 30, 2009. The next week I collaborated with John on the Dyson number puzzle, and that was the start of our yearlong association. I am grateful to John for giving me the privilege of bringing you the Monday puzzle as TierneyLab’s “Quiz Wiz.” Thank you, John. I’m sure our readers will join me in wishing you all the best for your column and the other things that you will be focusing on in the future.

To commemorate our year of puzzling together, we have four independent “cryptarithm” puzzles for our readers today. Their words tell the story of the past and the future of the Monday Puzzle. First, John gave me a setup on the net. He’s the best, and that’s the truth. Though TierneyLab will be no more, the Monday Puzzle will endure. We will continue to have a blast at our new location.Read more…

Will President Obama’s plan for space exploration bring us closer to Mars — or is it a step backward for those who favor human exploration of the solar system?

In my Findings column, I discuss some potential advantages of Mr. Obama’s plan to encourage private companies like SpaceX to take over some jobs formerly performed by NASA. You can read more about SpaceX and its president, Elon Musk, in this article by my colleague Ken Chang. I can understand people’s enduring affection for NASA — I still thrill to see the space shuttle take off — but I don’t think we’ll get to Mars unless entrepreneurs Mr. Musk can sharply reduce the costs of the journey.

I also recommend a thoughtful article in The New Atlantis by Rand Simberg, an aerospace engineer who runs the Transterrestrial Musings blog. In the article, he discusses ways to cut costs in space by shaking up NASA’s structure and by encouraging private companies. “Just as war is too important to be left to the generals, man’s future in space is too important to be left to NASA,” he writes, and elaborates:

We have had a monolithic government space agency for half a century at a cumulative cost of roughly half a trillion dollars (in current-year dollars). If we are going to continue to spend that order of magnitude of money—as, for political reasons, it seems we are going to do indefinitely—we should at least have something more to show for it than just a couple hundred brief trips to orbit for elite civil servants at an average cost over that period of about a couple billion dollars per flight. NASA needn’t do all the work of making space affordable and sustainable, but it ought to do something. To put it another way, it isn’t NASA’s job to put humans on Mars; it’s NASA’s job to make it possible for the National Geographic Society, or an offshoot of the Latter-Day Saints, or an adventure tourism company, to put humans on Mars.

Justin ThymeA bird lands on a string over a bowl of water. Will the bird get wet? (Mouse over the illustration for a hint. Click and hold for another hint. With the help of these hints, you can quickly figure out whether the bird will get wet or not without having to do any calculations.)

Hi folks. I’ve returned from my vacation, and the Monday Puzzle resumes today with a challenge to welcome the coming of Spring. It has been designed by our graphical maven, Justin Thyme. This puzzle continues on the theme of balance and slippage that characterized his previous contribution which became our most popular puzzle ever, the Slippery Slope Puzzle. Justin has also come up with an interesting game of strategy and suspense that hinges on guessing the number of comments this post will attract.

First, take a look at the very interesting illustration above, featuring a bird approaching a string that’s draped over two pulleys and attached to a golden weight at either end (in the shape of the sun and the moon respectively). Here are some facts about this setup:

A) The bowl of water is two feet wide.
B) The moon is six feet from the edge of the bowl closest to it.
C) The sun (golden globe resting on the bowl) and moon are at the same level.
D) The pulley over the moon is three times as high as the one over the sun as measured from the water’s surface.
E) The sun weighs two pounds. The moon and bird each weigh a pound.

1. The bird alights on the string, which sags under the bird’s weight. Assume that as the bird lands, it slides freely along the string. Will the bird slide over and land in the water, or will it stay dry? What will the final position of the moon be? (Assume that if the moon or sun gets lifted up all the way to the pulley, they get stuck there.)

Once you have solved the basic puzzle, there is scope for endless variations in this scenario. Read more…

In my Findings column, I discuss a study in Science that found wide cultural variations in concepts of fairness. It was measured by observing people in 15 societies around the world participate in a two-player game in which one player, called the dictator, decided how much of the prize to share with the other.

When this game was played in Hamilton, a small town in Missouri, the dictators gave away nearly half the prize — a division that probably sounds fair to you, since it’s a typical result when the experiment is tried in industrialized societies. But in this new far-flung study, hunter-gatherers, foragers, pastoralists and subsistence farmers were much less willing to share the prize, apparently because they didn’t feel an obligation to someone they didn’t know. Given the strength of family obligations in these traditional communities, they may well have considered it unfair to their own family if they gave away a prize to a stranger instead of bringing it home to their relatives.

After controlling for a variety of factors, the researchers — an international team of 14 anthropologists, psychologists and economists — identified two crucial predictors. People were more likely to share the prize if they were members of a “world religion” like Christianity or Islam, and, most important, if they lived in a community with high “market integration,” meaning that people bought most or all of their food. The researchers, led by Joseph Henrich of the University of British Columbia, suggest that participation in market transactions help establish norms of “fairness” toward strangers, and their conclusion was endorsed in a separate commentary in Science by Karla Hoff of the World Bank.

“I think that this is a very impressive study,” Dr. Hoff told me, noting that the results added to similar evidence from other traditional societies gathered earlier by Dr. Henrich and colleagues. In her commentary in Science, Dr. Hoff writes:

A society is not just a random group of people with a shared territory. It is a group that shares cognitive frames and social norms. We cannot know for certain how fairly our ancestors in foraging bands behaved in situations lacking relationship information, but Henrich et al. brings us a closer understanding by studying people in simple societies that may be very like those of our early ancestors. These findings call into question the standard assumption in economics that preferences are innate and stable, and suggests instead that cultural conditioning of the expression of human selfishness is a part of the process of economic development.

Dr. Hoff also mentions, in her commentary, a historical example of how norms of fairness contributed to economic growth: Read more…

Should Felix Baumgartner take a supersonic jump from a helium balloon 23 miles above the Earth? lf so, why?

I can think of one obvious explanation for jumping into the void: Because it’s not there. Or more simply: Because it’s cool. But I’m sure Lab readers can do better than that.

I discuss Mr. Baumgartner’s planned jump in my Findings column about him and the rest of the Red Bull Stratos team, which has been working for three years on this project. As NASA’s ambitions are being scaled back, private companies like Red Bull and Virgin Galactic and SpaceX have been working on new projects to get humans into space — or at least the edge of it, which Mr. Baumgartner hopes to reach in the stratosphere.

During his descent, he hopes to reach a speed of 690 miles per hour, which would break the speed of sound at that altitude and also break the speed record of 614 miles per hour (Mach 0.9) set by Joe Kittinger during his jump from 102,800 feet in 1960. Members of the Red Bull Stratos team, which includes Mr. Kittinger, say they want to do more than just break records, and that the lessons learned from their project can help save the lives of future astronauts and space tourists who run into trouble in the stratosphere.

But even without that practical justification, would this project still make sense? We’re a species that has prospered by taking risks, going farther, going faster. Is becoming the first human to break the speed of sound in free fall enough reason to step off that balloon? Is making the longest jump in history worthwhile just for its own sake?

Dave FergemannEach of these rectangles has the proportions of a familiar rectangular object. Can you recognize the objects by their proportions? (Each rectangle is drawn to a different scale.)

Today’s puzzle is about the ratios of small numbers—a subject that has fascinated mathematicians and artists alike. The entire puzzle and story, down to the interesting word-challenges, is an original creation of an All-Star puzzle solver, Dave Fergemann. I invite you to enjoy the feast that Dave has cooked up for us.

For our warm-up, we have a visual puzzle that is a sort of scavenger hunt.

1. Each of these rectangles shown in the figure above has the proportions of a familiar rectangular object. Can you recognize these objects by their proportions? Hint: Two are sports-related, two might be found in your home, and two might be part of your home.

Do you find some rectangles more attractive than others? Our main puzzle today is about a place where such preferences are religious… Read more…

Today we have some light fun based on the standard seven-segment number display used in digital LCD and LED clocks and calculators. The idea for this puzzle and some of the questions in it come from Dr. Kurt Eisemann, an emeritus mathematics professor from San Diego.

The standard seven-segment display of the ten digits is shown in the second line in the figure above.

1. Below are groups of digits whose calculator versions all have a particular property (or alternatively, do not have a property that all the other digits have). You have to figure out the characteristic property that the numbers in each group have (or don’t have):
a) 4, 5 and 6.
b) 3, 4 and 8.
c) 3, 4 and 7.

Last week we discussed the papaya battery, an utterly simple device whose geometry apparently creates a temperature difference where there was none before, thus violating the Second Law of Thermodynamics and creating potentially unlimited energy. In the field of thermodynamics, which abounds in apparent paradoxes, this is one of the most delicious paradoxes ever. Devices like the papaya battery, based on ellipsoids and parts of spheres, have been known to science since at least 1959 (J.C. Fallows in “New Scientist”) and have been discussed in the scientific literature in cutting-edge journals like the “Journal of Statistical Physics” and “Physics Bulletin” under the names “Ellipsoid Paradox” and “Chinese furnace” which interested readers can google.

In case anyone was misled by my tongue-in-cheek statements in last week’s blog, I must hasten to say that my brother Madhav and I were not the first ones to think up this paradox – we independently reconstructed it from a passing mention in a Scientific American article on entropy many years ago. Our contributions were in giving it its fruity name and we had fun coming up with compelling variations of it involving radial radiators and differently constructed bodies, which my brother demonstrated last week.

Of course, it doesn’t work, but the reason is not easy to see at first sight. In fact the papaya fails not because of any arcane physics but simply because of geometry: it fails because of the geometric equivalent of the dreaded division by zero. Read more…

This is a view of the solar system showing an unlabeled object whose orbit is shown in blue. You have to identify the object by solving today’s simple arithmetic puzzles.

After the heavy metal physics arguments about the papaya battery which are still ongoing, I thought we should relax with some lighter number music. Today’s problem requires nothing more than simple arithmetic and in one case, finding the square root. Today’s puzzle blog is based on problems devised by Dr. Aziz Inan, whom we met previously in Backdating.

Each of the first five problems below has a single target number, whose properties are described. In case of the first question, several numbers may satisfy the condition, but only one of them is the target number. You have to try and find the five unique numbers based on the clues contained in the other questions as well, since the numbers all hang together as described in the conditions.

1. The first number is a four-digit number such that when you divide it by ten you get a palindromic three digit number. When you add this three-digit number to the first number, you get a palindromic four digit number. [Extra question: How many such numbers are there?]

2. The second number is a four-digit number which is a perfect square. The square root can be obtained by subtracting the first number above from this second number and adding 4. [How many pairs of numbers satisfy the conditions in question 1 and 2?] Read more…

To salt or not to salt? To regulate right away or conduct more research first? My Findings column takes a skeptical look at the case for salt reduction. (You can also check out my colleague Jane Brody’s recent column on salt.) The salt wars can be vicious, pitting what I call the salt reformers against skeptics who say there isn’t enough evidence yet to justify public policies restricting salt levels. The reformers want immediate action; the skeptics want to see a randomized clinical trial. Your opinions are welcome.

For all the rancor, the two sides sometimes sound quite similar. They both, for instance, say that scientific studies of salt leave a lot to be desired — but they tend to mean the studies cited by the other side. If you mention the studies that show a low-salt diet is associated with worse clinical outcomes (as cited in this JAMA commentary), the salt reformers can reel off the methodological problems of that research.

But the salt skeptics can point to all kinds of problems with the reformers’ evidence, too, like the oft-repeated claim that Americans are eating more salt than they did previously (as stated, for instance, in this report from the Center for Science in the Public Interest, which advocates restricting salt). This supposed increase is based on surveys asking people’s recollections of what they ate. But the skeptics say that there isn’t a clear long-term trend in those numbers, and that the numbers themselves are suspect because they’re based on estimates based on people’s imperfect recollections of what they ate — and don’t include, for instance, how much salt people sprinkle on their food from a shaker.

The most precise way to chart daily salt consumption — the method used in the experiments involving low-sodium diets — is to measure the salt excreted in urine collected over a 24-hour period, and researchers on both sides say that these measures don’t reveal a clear upward trend in recent decades. The skeptics say the trend looks flat; the reformers say that they suspect consumption might be increasing, but that they can’t be sure.Read more…

Paul O’DonnellThe figure shows the inside of a revolutionary new invention, the papaya battery, that promises to solve all the world’s energy problems forever.

We’ve had a lot of quite sophisticated mathematical puzzles recently, like last week’s Case of the Carnival Cups, and the Toiling Antomatons and Stashing Llamas before that. Today we go on to something different, and far grander. I must announce that I have solved all the world’s problems. I’ve found the secret of making unlimited money with a simple scheme, and I’ve also figured out how to generate unlimited energy with my new invention, the papaya battery. Both these are based on the successful application of one of the deepest human principles of all time – getting something for nothing! To understand the papaya battery requires some physics, so let’s consider the money solution first.

Imagine two neighboring countries, much like the U.S.A. and Canada, that use dollars and cents as currency. Let’s call them A and B. Imagine that their exchange rate is such that an A-dollar has about the same value as a B-dollar. Now anyone who has traveled abroad knows that it’s a pain to keep converting just enough money to cover your stay. As a result, it’s sometimes more convenient to just use foreign money at say, a restaurant that accepts it. The catch is that you are always charged an arm and a leg for this convenience, and end up paying an exorbitant exchange rate. This is exactly the case at two border restaurants in countries A and B. They will accept the other country’s currency but require you to pay $1.25 to buy something that would cost $1 in the native currency.

A canny local entrepreneur (let’s just call him Canny) starts out in the morning with $10 in his pocket in country A, and buys coffee for A$1. He then catches tourists who have just arrived from country B and offers them A$9 in exchange for 10 B-dollars. Tourists are happy to comply, since they can easily get rid of their leftover foreign currency at a better rate than they would get in the restaurant. Then Canny walks across the border, and buys coffee in the restaurant in country B, offering his B$10 bill and getting B$9 as change. He offers this to a tourist who has just arrived from country A and is happy to get rid of $10 of his now inconvenient A-dollars for B$9. Canny then walks back across the border with the same amount of money he started with.

1. The tourists are happy to get rid of their excess foreign currency. The restaurants are happy to get paid in their own currency. Who then, pays for Canny’s coffee? Canny plans to open stalls outside both restaurants and make a big fortune. He can’t get away with this now, can ‘e?

The answers to these questions might reveal a great deal about what money really is. Read more…

The science rappers from Stanford are back. If you liked their take on regulatin’ genes, check out their new number on how the body converts food into energy. The song is performed by Derrick Davis, a student at Stanford, and Tom McFadden, an instructor in the human biology program there. Mr. McFadden (he’s the one wearing sunglasses and a plaid shirt in the video above) explained the project to me:

I’ve found that subjects like glycolysis, the citric acid cycle and the electron transport chain are some of the most feared and loathed concepts among people who’ve taken biology, mainly because some teachers emphasize memorization over concepts. Yet in reality, the way we turn “what we eat” into “what we do” is so relevant to everyone’s daily life that it ought to be inherently interesting. The video stylistically pays homage to two songs, “Hate it or Love it,” by 50 cent, and “On to the next one,” by Jay-Z. Once again, instead of bragging about stacks of cash we’re rapping about making “stacks” of ATP.”

At a carnival booth, our protagonist Tom is shown these numbered balls and has to determine the chances of getting the winning numbers.

Welcome to the season of wild and crazy celebrations. From Valentine’s Day yesterday, we pass on to Mardi Gras (or Carnival) tomorrow. In some countries like Brazil, Carnival is already well under way. Now the word “carnival” in the United States is also used to denote a traveling assemblage of entertainments, rides and games, like a country fair (or as it is called in other parts of the world, a funfair or fête). Today’s puzzle story is set in such a scene. Both the puzzle and the storyline are original contributions of our All-Star puzzle solver, Tom Enrico from Sandy, Utah. Here is Tom’s story:

We follow the adventures of a math student, Tommy MacMahon in a carnival. In the midst of the myriad bright lights, the blare of the calliope music from the carousel and the smell of popcorn, Tommy encounters a brightly-colored booth that offers various games of chance. Here he encounters his first challenge, which is our warm-up question.

1. The booth has a ball-randomizing machine that spits out four brightly colored balls numbered 1 through 4 in random order into a neat row. “Here are four balls in a row,” says the carnie in the booth. “Notice that these are arranged in the order 1,2,4,3 (as in the figure). If we compare each pair of balls, they are all in order except the pair 3,4 which is out of order because the larger number, 4, comes before the smaller one, 3. Here’s the deal: if the number of pairs that are out-of-order is less than two, you win one of these magnificent stuffed animal toys here.”
What are Tom’s chances of winning?

Note: You have to consider all six pairs of balls, not just adjacent ones.Read more…

About

John Tierney always wanted to be a scientist but went into journalism because its peer-review process was a great deal easier to sneak through. Now a columnist for the Science Times section, Tierney previously wrote columns for the Op-Ed page, the Metro section and the Times Magazine. Before that he covered science for magazines like Discover, Hippocrates and Science 86.

With your help, he's using TierneyLab to check out new research and rethink conventional wisdom about science and society. The Lab's work is guided by two founding principles:

Just because an idea appeals to a lot of people doesn't mean it's wrong.

But that's a good working theory.

Comments and suggestions are welcome, particularly from researchers with new findings. E-mail tierneylab@nytimes.com.